{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## BO with Warped Gaussian Processes\n",
        "\n",
        "In this tutorial, we illustrate how to use learned input warping functions for robust Bayesian Optimization when the outcome may be non-stationary functions. When the lengthscales are non-stationarity in the raw input space, learning a warping function that maps raw inputs to a warped space where the lengthscales are stationary can be useful, because then standard stationary kernels can be used to effectively model the function.\n",
        "\n",
        "In general, for a relatively simple setup (like this one), we recommend using [Ax](https://ax.dev), since this will simplify your setup (including the amount of code you need to write) considerably. See Ax's [Modular BoTorch tutorial](https://ax.dev/docs/tutorials/modular_botorch/) tutorial. To use input warping with `MODULAR_BOTORCH`, we can pass the `warp_tf`, constructed as below, by adding `input_transform=warp_tf` argument to the `Surrogate(...)` call. \n",
        "\n",
        "We consider use a Kumaraswamy CDF as the class of input warping function and learn the concentration parameters ($a>0$ and $b>0$). Kumaraswamy CDFs are quite flexible and map inputs in [0, 1] to outputs in [0, 1]. This work follows the Beta CDF input warping proposed by Snoek et al., but replaces the Beta distribution Kumaraswamy distribution, which has a *differentiable* and closed-form CDF. \n",
        "   \n",
        "   $$K_\\text{cdf}(x) = 1 - (1-x^a)^b$$\n",
        "   \n",
        "This enables maximum likelihood (or maximum a posteriori) estimation of the CDF hyperparameters using gradient methods to maximize the likelihood (or posterior probability) jointly with the GP hyperparameters. (Snoek et al. use a fully Bayesian treatment of the CDF parameters). Each input dimension is transformed using a separate warping function.\n",
        "\n",
        "We use the Log Noisy Expected Improvement (qLogNEI) acquisition function to optimize a synthetic Hartmann6 test function. The standard problem is\n",
        "\n",
        "$$f(x) = -\\sum_{i=1}^4 \\alpha_i \\exp \\left( -\\sum_{j=1}^6 A_{ij} (x_j - P_{ij})^2  \\right)$$\n",
        "\n",
        "over $x \\in [0,1]^6$ (parameter values can be found in `botorch/test_functions/hartmann6.py`). For this demonstration,\n",
        "We first warp each input dimension through a different inverse Kumaraswamy CDF.\n",
        "\n",
        "Since BoTorch assumes a maximization problem, we will attempt to maximize $-f(x)$ to achieve $\\max_{x} -f(x) = 3.32237$.\n",
        "\n",
        "[1] [J. Snoek, K. Swersky, R. S. Zemel, R. P. Adams. Input Warping for Bayesian Optimization of Non-Stationary Functions. Proceedings of the 31st International Conference on Machine Learning, PMLR 32(2):1674-1682, 2014.](http://proceedings.mlr.press/v32/snoek14.pdf)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "# Install dependencies if we are running in colab\n",
        "import sys\n",
        "if 'google.colab' in sys.modules:\n",
        "    %pip install botorch"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {},
      "outputs": [],
      "source": [
        "import os\n",
        "import torch\n",
        "\n",
        "\n",
        "device = torch.device(\"cuda\" if torch.cuda.is_available() else \"cpu\")\n",
        "dtype = torch.double\n",
        "SMOKE_TEST = os.environ.get(\"SMOKE_TEST\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Problem setup\n",
        "\n",
        "First, we define the sample parameters for the sigmoid functions that transform the respective inputs."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'Transformed Value')"
            ]
          },
          "execution_count": 5,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
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",
            "text/plain": [
              "<Figure size 500x500 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "from torch.distributions import Kumaraswamy\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "%matplotlib inline\n",
        "\n",
        "\n",
        "fontdict = {\"fontsize\": 15}\n",
        "torch.manual_seed(1234567890)\n",
        "c1 = torch.rand(6, dtype=dtype, device=device) * 3 + 0.1\n",
        "c0 = torch.rand(6, dtype=dtype, device=device) * 3 + 0.1\n",
        "x = torch.linspace(0, 1, 101, dtype=dtype, device=device)\n",
        "k = Kumaraswamy(concentration1=c1, concentration0=c0)\n",
        "k_icdfs = k.icdf(x.unsqueeze(1).expand(101, 6))\n",
        "fig, ax = plt.subplots(1, 1, figsize=(5, 5))\n",
        "\n",
        "for i in range(6):\n",
        "    ax.plot(x.cpu(), k_icdfs[:, i].cpu())\n",
        "ax.set_xlabel(\"Raw Value\", **fontdict)\n",
        "ax.set_ylabel(\"Transformed Value\", **fontdict)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {},
      "outputs": [],
      "source": [
        "from botorch.test_functions import Hartmann\n",
        "\n",
        "neg_hartmann6 = Hartmann(negate=True)\n",
        "\n",
        "\n",
        "def obj(X):\n",
        "    X_warp = k.icdf(X)\n",
        "    return neg_hartmann6(X_warp)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "#### Initial design\n",
        "\n",
        "The models are initialized with 14 points in $[0,1]^6$ drawn from a scrambled sobol sequence.\n",
        "\n",
        "We observe the objectives with additive Gaussian noise with a standard deviation of 0.05."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {},
      "outputs": [],
      "source": [
        "from botorch.models import SingleTaskGP\n",
        "from gpytorch.mlls.sum_marginal_log_likelihood import ExactMarginalLogLikelihood\n",
        "from botorch.utils.sampling import draw_sobol_samples\n",
        "\n",
        "NOISE_SE = 0.05\n",
        "train_yvar = torch.tensor(NOISE_SE**2, device=device, dtype=dtype)\n",
        "\n",
        "bounds = torch.tensor([[0.0] * 6, [1.0] * 6], device=device, dtype=dtype)\n",
        "\n",
        "\n",
        "n = 14\n",
        "# generate initial training data\n",
        "train_x = draw_sobol_samples(\n",
        "    bounds=bounds, n=n, q=1, seed=torch.randint(0, 10000, (1,)).item()\n",
        ").squeeze(1)\n",
        "exact_obj = obj(train_x).unsqueeze(-1)  # add output dimension\n",
        "\n",
        "best_observed_value = exact_obj.max().item()\n",
        "train_obj = exact_obj + NOISE_SE * torch.randn_like(exact_obj)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "#### Input warping and model initialization\n",
        "We initialize the `Warp` input transformation and pass it a `SingleTaskGP` to model the noiseless objective. The `Warp` object is a `torch.nn.Module` that contains the concentration parameters and applies the warping function in the `Model`'s `forward` pass."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {},
      "outputs": [],
      "source": [
        "from botorch.models.transforms.input import Warp\n",
        "from gpytorch.priors.torch_priors import LogNormalPrior\n",
        "\n",
        "\n",
        "def initialize_model(train_x, train_obj, bounds):\n",
        "    # initialize input_warping transformation\n",
        "    warp_tf = Warp(\n",
        "        d=train_x.shape[-1],\n",
        "        indices=list(range(train_x.shape[-1])),\n",
        "        # use a prior with median at 1.\n",
        "        # when a=1 and b=1, the Kumaraswamy CDF is the identity function\n",
        "        concentration1_prior=LogNormalPrior(0.0, 0.75**0.5),\n",
        "        concentration0_prior=LogNormalPrior(0.0, 0.75**0.5),\n",
        "        bounds=bounds,\n",
        "    )\n",
        "    # define the model for objective\n",
        "    model = SingleTaskGP(\n",
        "        train_X=train_x,\n",
        "        train_Y=train_obj,\n",
        "        train_Yvar=train_yvar.expand_as(train_obj),\n",
        "        input_transform=warp_tf,\n",
        "    ).to(train_x)\n",
        "    mll = ExactMarginalLogLikelihood(model.likelihood, model)\n",
        "    return mll, model"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "#### Define a helper function that performs the essential BO step\n",
        "The helper function below takes an acquisition function as an argument, optimizes it, and returns the batch $\\{x_1, x_2, \\ldots x_q\\}$ along with the observed function values. For this example, we'll use sequential $q=1$ optimization. A simple initialization heuristic is used to select the 20 restart initial locations from a set of 512 random points. "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {},
      "outputs": [],
      "source": [
        "from botorch.optim import optimize_acqf\n",
        "\n",
        "\n",
        "num_restarts = 20 if not SMOKE_TEST else 2\n",
        "raw_samples = 512 if not SMOKE_TEST else 32\n",
        "\n",
        "\n",
        "def optimize_acqf_and_get_observation(acq_func):\n",
        "    \"\"\"Optimizes the acquisition function, and returns a new candidate and a noisy observation.\"\"\"\n",
        "    # optimize\n",
        "    candidates, _ = optimize_acqf(\n",
        "        acq_function=acq_func,\n",
        "        bounds=bounds,\n",
        "        q=1,\n",
        "        num_restarts=num_restarts,\n",
        "        raw_samples=raw_samples,  # used for intialization heuristic\n",
        "        options={\"batch_limit\": 5, \"maxiter\": 200},\n",
        "    )\n",
        "    # observe new values\n",
        "    new_x = candidates.detach()\n",
        "    exact_obj = obj(new_x).unsqueeze(-1)  # add output dimension\n",
        "    train_obj = exact_obj + NOISE_SE * torch.randn_like(exact_obj)\n",
        "    return new_x, train_obj\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Perform Bayesian Optimization\n",
        "The Bayesian optimization loop iterates the following steps:\n",
        "1. given a surrogate model, choose a candidate point $x$\n",
        "2. observe $f(x)$\n",
        "3. update the surrogate model. \n",
        "\n",
        "We do `N_BATCH=50` rounds of optimization."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            ".................................................."
          ]
        }
      ],
      "source": [
        "from botorch import fit_gpytorch_mll\n",
        "from botorch.acquisition.logei import qLogNoisyExpectedImprovement\n",
        "from botorch.exceptions import BadInitialCandidatesWarning\n",
        "\n",
        "import warnings\n",
        "\n",
        "warnings.filterwarnings(\"ignore\", category=BadInitialCandidatesWarning)\n",
        "warnings.filterwarnings(\"ignore\", category=RuntimeWarning)\n",
        "\n",
        "N_BATCH = 50 if not SMOKE_TEST else 5\n",
        "\n",
        "torch.manual_seed(0)\n",
        "\n",
        "best_observed = [best_observed_value]\n",
        "mll, model = initialize_model(train_x, train_obj, bounds)\n",
        "\n",
        "# run N_BATCH rounds of BayesOpt after the initial random batch\n",
        "for iteration in range(1, N_BATCH + 1):\n",
        "\n",
        "    # fit the models\n",
        "    fit_gpytorch_mll(mll)\n",
        "    ei = qLogNoisyExpectedImprovement(model=model, X_baseline=train_x)\n",
        "\n",
        "    # optimize and get new observation\n",
        "    new_x, new_obj = optimize_acqf_and_get_observation(ei)\n",
        "\n",
        "    # update training points\n",
        "    train_x = torch.cat([train_x, new_x])\n",
        "    train_obj = torch.cat([train_obj, new_obj])\n",
        "\n",
        "    # update progress\n",
        "    best_value = obj(train_x).max().item()\n",
        "    best_observed.append(best_value)\n",
        "\n",
        "    mll, model = initialize_model(train_x, train_obj, bounds)\n",
        "\n",
        "    print(\".\", end=\"\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "#### Plot the results\n",
        "The plot below shows the log regret at each step of the optimization for each of the algorithms."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'Log10 Regret')"
            ]
          },
          "execution_count": 11,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 800x600 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "import numpy as np\n",
        "from matplotlib import pyplot as plt\n",
        "\n",
        "%matplotlib inline\n",
        "\n",
        "\n",
        "GLOBAL_MAXIMUM = neg_hartmann6.optimal_value\n",
        "\n",
        "iters = np.arange(N_BATCH + 1)\n",
        "y_ei = np.log10(GLOBAL_MAXIMUM - np.asarray(best_observed))\n",
        "\n",
        "fig, ax = plt.subplots(1, 1, figsize=(8, 6))\n",
        "\n",
        "ax.plot(\n",
        "    iters,\n",
        "    y_ei,\n",
        "    linewidth=1.5,\n",
        "    alpha=0.6,\n",
        ")\n",
        "\n",
        "ax.set_xlabel(\"number of observations (beyond initial points)\")\n",
        "ax.set_ylabel(\"Log10 Regret\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": []
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "python3",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.7.11"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 2
}
